If anything, shouldn’t that drive prices down, as landlords now know exactly how much to undercut their competitors to still make a profit but also get more rapid turnover? I thought microeconomic competitive market theory assumes that more information is always a positive influence on markets, at least for the simplified models. Is RealPage a counter example?

The agreement between RealPage and the landlord is that they do not undercut RealPage's recommended rent amount.

To use RealPage you have to agree to not sell below their algorithmic price.

So why is there a housing shortage?

It is not a real supply shortage: number of families has not gone up and number of homes has not decreased. It is just increase of demand side, probably due to the printed new money and income increase. People could just live as before but their appetite has grown and it pushes demand up.

NIMBYs, mostly.

Is there? Every time I've looked into this the numbers don't tell that story.

What we do see is landlords (corporate and private) taking things off the market on purpose to keep prices up, in addition to the collusion this thread is actively talking about.

By every conceivable metric housing has kept up with population.

Shortage? No.

Constructed scenarios that force people to lower their standard of living so landlords can make more money? Yes.